================================================================================ Nomenclature ================================================================================ .. list-table:: :header-rows: 1 :align: center :widths: auto * - Symbols - Definition - Units * - :math:`A` - Atom fraction, e.g., Eq. (:ref:`10.3-7<eq-10.3-7>`) or coefficients of the quadratic function of temperature for fuel thermal conductivity, e.g., Eqs. (:ref:`10.3-52<eq-10.3-52>`) and (:ref:`10.3-61<eq-10.3-61>`). - * - :math:`a` - Atomic weight - * - :math:`B` - Coefficient of the quadratic function of temperature for fuel thermal conductivity, e.g., Eqs. (:ref:`A10.2-1<eq-A10.2-1>`) to (:ref:`A10.2-3<eq-A10.2-3>`) - * - :math:`Bu` - Fuel burnup - atom % * - :math:`C` - Plutonium alloying coefficient in thermal conductivity Eq. (:ref:`10.3-102<eq-10.3-102>`) - * - :math:`C_{\text{p}}` - Specific heat - J/kg-K * - :math:`c` - Coefficient of the quadratic term in the simplified enthalpy Eq. (:ref:`10.3-26<eq-10.3-26>`) - * - :math:`D` - Value of determinants in Cramer's rule for solving a system of linear algebraic equations - * - :math:`f_{\text{o}}` - Heavy-metal mass fissioned expressed as a percentage of U-Pu-Zr alloy post-irradiation mass - * - :math:`H` - Enthalpy - J/mol * - :math:`h` - Enthalpy - J/kg * - :math:`K` - Thermal Conductivity - W/m-K * - :math:`K_{\text{pt}1}` - Thermal conductivity of a pore tube containing a fission gas-filled pore - W/m-K * - :math:`K_{\text{pt}2}` - Thermal conductivity of a pore tube containing a logged sodium-filled pore - W/m-K * - :math:`L` - Length, e.g., Eq. (:ref:`10.3-44<eq-10.3-44>`) or Lorenz number in Q. (:ref:`10.3-68<eq-10.3-68>`) - m W-Ω/K\ :sup:`2` * - :math:`M` - Mass - kg * - :math:`m_{\text{a}}` - One atomic mass unit, :math:`1.6592828 \times 10^{-27}` kg - kg * - :math:`N` - Number of atoms, e.g., Eq. (:ref:`10.3-34<eq-10.3-34>`) or number of fissions, e.g., Eq. (:ref:`10.3-35<eq-10.3-35>`) or number of pairs of temperature and enthalpy values, e.g., Eq. (:ref:`10.3-37<eq-10.3-37>`) - * - :math:`Na` - Avogadro's number, :math:`6.02472 \times 10^{26}` molecules/kg-mole - /kg-mole * - :math:`P'` - Porosity fraction relative to the 100%-dense volume - * - :math:`P_{\text{c}1}` - Areal fraction of a face of a unit cell that is occupied by a sodium-filled pore, e.g., Eq. (:ref:`10.3-72<eq-10.3-72>`) - * - :math:`P_{\text{c}2}` - Areal fraction of a face of a unit cell that is occupied by a sodium-filled pore, e.g., Eq. (:ref:`10.3-72<eq-10.3-72>`) - * - :math:`P_{\text{g}}` - Gas-filled porosity fraction relative to the swollen fuel volume - * - :math:`P_{\text{I},1}` - Fraction of the side (in heat flow direction) of a unit cell that is occupied by a gas-filled pore - * - :math:`P_{\text{I},2}` - Fraction of the side (in heat flow direction) of a unit cell that is occupied by a sodium-filled pore - * - :math:`P_{\text{Na}}` - Sodium-filled porosity fraction relative to the swollen fuel volume - * - :math:`T` - Temperature - K * - :math:`V` - Volume - m\ :sup:`3` * - :math:`v` - Characteristic volume of an atom - m\ :sup:`3` * - :math:`W` - Weight fraction - * - :math:`X_{\text{i}}` - Weight fractions of the 3 database alloys to be mixed to produce the desired fuel composition - * - :math:`x` - Zr weight fraction in the U-Zr binary database alloy used in enthalpy region 1 or thermal conductivity region 3 - * - :math:`Y_{\text{i}}` - Atom fractions of the 3 database alloys to be mixed to produce the desired fuel composition - * - :math:`\alpha` - Coefficient of linear thermal expansion - per K * - :math:`\Delta L` - Linear thermal expansion from 293K - m * - :math:`\rho` - Density, e.g., Eq. (:ref:`10.3-32<eq-10.3-32>`) or electrical resistivity in Eq. (:ref:`10.3-68<eq-10.3-68>`) - kg/m\ :sup:`3` Ω-m * - :math:`\sigma` - Standard deviation - * - Subscripts: - - * - :math:`\text{a}` - Desired alloy or desired database alloy - * - :math:`\text{c}` - Centigrade temperature scale - * - :math:`\text{f}` - Fission, e.g., Eq. (:ref:`10.3-38<eq-10.3-38>`) or solid fission products, e.g., Eq. (:ref:`10.3-40<eq-10.3-40>`) or desired fuel, e.g., Eq. (:ref:`10.3-61<eq-10.3-61>`) - * - :math:`\text{g}` - Fission gas - * - :math:`\text{h}` - Heavy metals - * - :math:`\text{i}` - Index for fuel constituents (I - U, Pu, Zr) or index for the 3 database alloys of a region of interpolation - * - :math:`\text{l}` - Liquidus or molten liquid - * - :math:`\text{Na}` - Sodium - * - :math:`\text{o}` - Fabricated condition, e.g., Eq. (:ref:`10.3-33<eq-10.3-33>`) or 100%-dense unirradiated condition, e.g., Eq. (:ref:`10.3-72<eq-10.3-72>`) or a specified temperature, e.g., Eq. (:ref:`10.3-44<eq-10.3-44>`) - * - :math:`\text{p}` - Plutonium - * - :math:`\text{s}` - Solidus - * - :math:`\text{sfp}` - Solid fission products - * - :math:`\text{th}` - Theoretical - * - :math:`\text{u}` - Uranium - * - :math:`\text{uz}` - U-Zr binary alloy - * - :math:`\text{u50}` - U-50 atom % Zr binary alloy - * - :math:`\text{z}` - Zirconium - * - :math:`\alpha` - Lowest-temperature solid-state phase (α-phase) - * - :math:`\gamma` - Highest-temperature solid-state phase (γ-phase) -